Reduction of acyclic phase-type representations [article]

Muhammad Reza Pulungan, Universität Des Saarlandes, Universität Des Saarlandes
2009
Acyclic phase-type distributions are phase-type distributions with triangular matrix representations. They constitute a versatile modelling tool, since they (1) can serve as approximations to any continuous probability distribution, and (2) exhibit special properties and characteristics that usually make their analysis easier. The size of the matrix representations has a strong effect on the computational efforts needed in analyzing these distributions. These representations, however, are not
more » ... however, are not unique, and two representations of the same distribution can differ drastically in size. This thesis proposes an effective algorithm to reduce the size of the matrix representations without altering their associated distributions. The algorithm produces significantly better reductions than existing methods. Furthermore, the algorithm consists in only standard numerical computations, and therefore is straightforward to implement. We identify three operations on acyclic phase-type representations that arise often in stochastic models. Around these operations we develop a simple stochastic process calculus, which provides a framework for stochastic modelling and analysis. We prove that the representations produced by the three operations are "almost surely" minimal, and the reduction algorithm can be used to obtain these almost surely minimal representations. The applicability of these contributions is exhibited on a variety of case studies. v First and foremost, I thank my supervisor Holger Hermanns for his patience and diligence in guiding me throughout my years in Saarbrücken. He has been an excellent mentor who is ever ready for discussions. I would also like to thank my colleagues in the group:
doi:10.22028/d291-25951 fatcat:d5xk7vp5fjd37mzy2r4wbverse